Question

Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a face - centred cubic (fcc) structure. (Atomic mass of Al = 27 g $mo{l}^{-1}$)

Answer 1

Moles of aluminium $=\frac{\text{Mass}}{\text{Molecular mass}}$
$n_{AI}=\frac{8.1}{27}=0.3moles$
We know that one unit of fcc, No. of atoms = 4
4 atoms are found in unit cell = 1
1 atom is found in unit cell $=\frac{1}{4}$
(1 mole) $N_A$ atoms are found in unit cell $=\frac{N_A}{4}$
0.3 moles atoms are found in unit cell $=\frac{N_A}{4}\times 0.3$
$=0.75\times N_A$
$=4.5\times {10}^{23}atoms$